What is he best known for?
The fields of study he is best known for:
- Quantum mechanics
- Mathematical analysis
- Statistics
Mechanics, Mathematical analysis, Classical mechanics, Reynolds number and Applied mathematics are his primary areas of study.
His Mechanics study frequently draws connections between related disciplines such as Cylinder.
His biological study spans a wide range of topics, including Stochastic process and Monte Carlo method, Polynomial chaos.
The concepts of his Classical mechanics study are interwoven with issues in Dissipative particle dynamics, Heat transfer, Hele-Shaw flow, Direct numerical simulation and Flow visualization.
His Reynolds number research incorporates elements of Flow, Navier–Stokes equations, Laminar flow and Amplitude.
The various areas that George Em Karniadakis examines in his Applied mathematics study include Galerkin method, Nonlinear system, Compressibility, Mathematical optimization and Discretization.
His most cited work include:
- The Wiener--Askey Polynomial Chaos for Stochastic Differential Equations (3207 citations)
- High-order splitting methods for the incompressible Navier-Stokes equations (1126 citations)
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (1079 citations)
What are the main themes of his work throughout his whole career to date?
His scientific interests lie mostly in Mechanics, Mathematical analysis, Applied mathematics, Classical mechanics and Flow.
As part of his studies on Mechanics, George Em Karniadakis often connects relevant areas like Dissipative particle dynamics.
His studies in Dissipative particle dynamics integrate themes in fields like Mesoscopic physics and Hagen–Poiseuille equation.
His Mathematical analysis research is multidisciplinary, incorporating perspectives in Stochastic process and Polynomial chaos.
His Applied mathematics study integrates concerns from other disciplines, such as Artificial neural network, Mathematical optimization and Nonlinear system.
His Artificial neural network research integrates issues from Algorithm, Deep learning, Partial differential equation and Inverse problem.
He most often published in these fields:
- Mechanics (24.00%)
- Mathematical analysis (14.29%)
- Applied mathematics (13.73%)
What were the highlights of his more recent work (between 2018-2021)?
- Artificial neural network (9.82%)
- Applied mathematics (13.73%)
- Inverse problem (4.24%)
In recent papers he was focusing on the following fields of study:
George Em Karniadakis focuses on Artificial neural network, Applied mathematics, Inverse problem, Artificial intelligence and Nonlinear system.
His Artificial neural network research is multidisciplinary, relying on both Uncertainty quantification, Algorithm and Partial differential equation.
His Applied mathematics research incorporates themes from Operator, Boundary value problem, Space, Discretization and Function.
His research in Inverse problem intersects with topics in Acoustics, Euler equations, Inverse, Finite element method and Hyperparameter.
His Artificial intelligence research is multidisciplinary, incorporating elements of Machine learning and Physical law.
His work on Nonlinear system is being expanded to include thematically relevant topics such as Conservation law.
Between 2018 and 2021, his most popular works were:
- Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations (1079 citations)
- Hidden fluid mechanics: Learning velocity and pressure fields from flow visualizations. (158 citations)
- Deep learning of vortex-induced vibrations (103 citations)
In his most recent research, the most cited papers focused on:
- Quantum mechanics
- Statistics
- Artificial intelligence
His primary scientific interests are in Artificial neural network, Applied mathematics, Nonlinear system, Artificial intelligence and Deep learning.
George Em Karniadakis has included themes like Algorithm, Partial differential equation and Inverse problem in his Artificial neural network study.
His research integrates issues of Domain decomposition methods, Space, Discretization, Function and Domain in his study of Applied mathematics.
George Em Karniadakis does research in Nonlinear system, focusing on Burgers' equation specifically.
His study looks at the relationship between Finite element method and fields such as Navier–Stokes equations, as well as how they intersect with chemical problems.
George Em Karniadakis combines subjects such as Stochastic differential equation and Mathematical optimization with his study of Stochastic process.
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